Electromagnetic Modeling of Dielectric Mixtures

Luigi La Spada; Renato Iovine; Lucio Vegni

doi:10.6000/1929-5995.2013.02.04.2

Authors

Luigi La Spada Department of Engineering, University of Roma Tre, Via Vito Volterra 62, 00146, Rome, Italy
Renato Iovine Department of Engineering, University of Roma Tre, Via Vito Volterra 62, 00146, Rome, Italy
Lucio Vegni Department of Engineering, University of Roma Tre, Via Vito Volterra 62, 00146, Rome, Italy

DOI:

https://doi.org/10.6000/1929-5995.2013.02.04.2

Keywords:

Analytical models, dielectric mixtures, effective permittivity, dispersive models, polymers

Abstract

Electromagnetic modeling of dielectric materials allows us to study the effects of electromagnetic wave propagation and how such electromagnetic fields influence and interact with them.

Dielectric materials are composites or mixtures, which often are made up of at least two constituents or phases. Modelling the electromagnetic behaviour of dielectric mixtures is crucial to understand how geometrical factors (shape and concentration), electromagnetic properties of inclusions and background medium, influence the permittivity of the overall material.

The aim of this work is to develop new analytical models for dielectric mixtures, in order to describe their electromagnetic behaviour and design them with desired electromagnetic properties, for specific required applications. In particular, in this paper a new general expression for the effective permittivity of dielectric mixture is presented. The mixtures consist of inclusions, with arbitrary shapes, embedded in a surrounding dielectric environment. We consider the hosting environment and the hosted material as real dielectrics, both of them as dispersive dielectrics.

The proposed analytical models simplify practical design tasks for dielectric mixtures and allow us to understand their physical phenomena and electromagnetic behaviours.

References

Pendry JB. Playing Tricks with Light. Science 1999; 285: 1687-88. http://dx.doi.org/10.1126/science.285.5434.1687 DOI: https://doi.org/10.1126/science.285.5434.1687

Chau YF, Jiang ZH, Li HY, Lin GM, Wu FL, Lin WH. Localized resonance of composite core-shell nanospheres, nanobars and nanospherical chains. Progr Electromagnet Res 2011; 28: 183-99. DOI: https://doi.org/10.2528/PIERB10102705

Maier SA, Kik PG, Atwater HA, Meltzer S, Harel E, Koel BE, Requicha AG. Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides. Nat Mater 2003; 2: 229-32. http://dx.doi.org/10.1038/nmat852 DOI: https://doi.org/10.1038/nmat852

Riboh JC, Haes AJ, McFarland AD, Ranjit C, Van Duyne RP. A Nanoscale Optical Biosensor: Real Time Immunoassay and Nanoparticle Adhesion. J Phys Chem B 2003; 107: 1772-80. http://dx.doi.org/10.1021/jp022130v DOI: https://doi.org/10.1021/jp022130v

Bukasov R, Ali TA, Nordlander P, Shumaker-Parry JS. Probing the plasmonic near-field of gold nanocrescent antennas. ACS Nano 2010; 4: 6639-50. http://dx.doi.org/10.1021/nn101994t DOI: https://doi.org/10.1021/nn101994t

Storhoff JJ, Elghanian R, Mucic RC, Mirkin CA, Letsinger RL. DNA Directed Synthesis of Binary Nanoparticle Network Materials. J Am Chem Soc 1998; 120: 12674-5. http://dx.doi.org/10.1021/ja982721s DOI: https://doi.org/10.1021/ja982721s

Larsson EM, Alegret J, Kall M, Sutherland DS. Sensing characteristics of NIR localized surface plasmon resonances in gold nanoring for application as ultrasensitive biosensors. Nano Lett 2007; 7: 1256-63. http://dx.doi.org/10.1021/nl0701612 DOI: https://doi.org/10.1021/nl0701612

Galush WJ, Shelby SA, Mulvihill MJ, Tao A, Yang P, Groves JT. A nanocube plasmonic sensor for molecular binding on membrane surfaces. Nano Lett 2009; 9: 2077-82. http://dx.doi.org/10.1021/nl900513k DOI: https://doi.org/10.1021/nl900513k

Rosi NL, Mirkin CA. Nanostructures in biodiagnostics. Chem Rev 2005; 105: 1547-62. http://dx.doi.org/10.1021/cr030067f DOI: https://doi.org/10.1021/cr030067f

Chen J, Wiley BJ, Cang H, Campbell D, Saeki F, Au L, et al. Gold Nanocages: Engineering the Structures for Biomedical Applications. Adv Mater 2005; 17: 2255-61. http://dx.doi.org/10.1002/adma.200500833 DOI: https://doi.org/10.1002/adma.200500833

Hiep HM, Endo T, Kerman K, Chikae M, Kim DK, Yamamura S, et al. A localized surface plasmon resonance based immunosensor for the detection of casein in milk. Sci Technol Adv Mater 2007; 8: 331-38. http://dx.doi.org/10.1016/j.stam.2006.12.010 DOI: https://doi.org/10.1016/j.stam.2006.12.010

Yelin D, Oron D, Thiberge S, Moses E, Silberberg Y, Willner I. Multiphoton plasmon-resonance microscopy. Opt Express 2003; 11: 1385-91. http://dx.doi.org/10.1364/OE.11.001385 DOI: https://doi.org/10.1364/OE.11.001385

Sokolov K, Follen M, Aaron J, Pavlova I, Malpica A, Lotan R, Richards-Kortum R. Real-Time Vital Optical Imaging of Precancer Using Anti-Epidermal Growth Factor Receptor Antibodies Conjugated to Gold Nanoparticles. Cancer Res 2003; 63: 1999-2004.

Bohren C, Huffmann D. Absorption and Scattering of Light by Small Particles. New-York, John Wiley 1983.

Yaghjian AD. Electric dyadic Green’s functions in the source region. Proc IEEE 1980; 68: 248-63. http://dx.doi.org/10.1109/PROC.1980.11620 DOI: https://doi.org/10.1109/PROC.1980.11620

Avelin J, Arslan AN, Brännback J, Flykt M, Icheln C, Juntunen J, et al. Electric fields in the source region: the depolarization dyadic for a cubic cavity. Electr Eng 1998; 81: 199-202. http://dx.doi.org/10.1007/BF01233270 DOI: https://doi.org/10.1007/BF01233270

Landau LD, Lifshitz EM. Electrodynamics of Continuous Media. Oxford, Pergamon Press 1984. DOI: https://doi.org/10.1016/B978-0-08-030275-1.50007-2

Van Bladel JG. Electromagnetic Fields. Hoboken, John Wiley & Sons 2007. http://dx.doi.org/10.1002/047012458X DOI: https://doi.org/10.1002/047012458X

Sihvola A. Dielectric Polarization and Particle Shape Effects. J Nanomater 2007; 1: 1-9. http://dx.doi.org/10.1155/2007/45090 DOI: https://doi.org/10.1155/2007/45090

Sihvola A. Electromagnetic Mixing Formulas and Applications. London, The Institution of Engineering and Technology 2008.

Kasarova SN, Sultanova NG, Ivanov CD, Nikolov ID. Analysis of the dispersion of optical plastic materials. Optic Mater 2007; 29: 1481-90. http://dx.doi.org/10.1016/j.optmat.2006.07.010 DOI: https://doi.org/10.1016/j.optmat.2006.07.010

Kuzmenko AB. Kramers–Kronig constrained variational analysis of optical spectra. Rev Sci Instrum 2005; 76: 083108.1-9. DOI: https://doi.org/10.1063/1.1979470

Yamamoto K. Optical theory applied to infrared spectroscopy. Vib Spectros 1994; 8: 1-36. http://dx.doi.org/10.1016/0924-2031(94)00022-9 DOI: https://doi.org/10.1016/0924-2031(94)00022-9

Rakic AD, Djurisic AB, Elazar JM, Majewski ML. Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl Opt 1998; 37: 5271-83. http://dx.doi.org/10.1364/AO.37.005271 DOI: https://doi.org/10.1364/AO.37.005271

Blythe AR. Electrical Properties Of Polymers. Cambridge, Cambridge University Press 2005.

Jitian S, Bratu I. Determination of optical constants of polymethyl methacrylate films from IR reflection-absorption spectra. Proceedings of AIP Conferences 2012; 1425: 26-29. http://dx.doi.org/10.1063/1.3681958 DOI: https://doi.org/10.1063/1.3681958